I have yet to start a campaign but in all instances of the rules it always says that you start a campaign with the Aftermath Mission. So say our group plays through an entire campaign and wants to start a new one, are you always required to use Aftermath as the starting mission or is there a method to picking a new starting mission?

As published, Aftermath will always be your starting point. The following side mission will be random. The story mission after that could be the same or different depending on who wins aftermath in your two campaigns.

In my opinion, switching up heroes, buying different gear and class cards, and having a different class deck for the Imperials will provide a fair bit of replayability. Plus, many missions have multiple possible events at a single trigger from which he Imperial Player only chooses 1. Being able to choose a different option in subsequent playthroughs keeps suspense up and adds to the excitement.

Of course, there is nothing preventing you from making your own scenario to start off a campaign.

You always want to start with Aftermath. The first reason being that the outcome of that mission decides what the second mission is. Second, you get money, exp and influence from that mission. I guess there's nothing saying you couldn't skip Aftermath and then play the mission you didn't play the first time, giving the appropriate rewards for what would be the winning side. But I wouldn't recommend it. Even in Aftermath the Imperial player has different choices to make at different times. So even though it's the same mission it can still feel different than the first time.